Protractor



P. F. BOEHM Dec. 23, 1952 PROTRACTOR Filed Dec. 10, 1945 Q14?. mv

Patented Dec. 23, 1952 PROTRACTOR laul tFwoehm, Greenwich, Conn., assigner to .JohnfR..Cassell.Co., Incorporated, New York, N.` Y., a. corporation of NewYork ApplicationLDecember 10, 1945, Serial.No.33,98'7

(Cl. .3S-.1)

.3, Claims.

The present invention :refers to protractors, andmore specically toprotractorsadaptedtobe used in connection with *.axencmetrie drawings- It is one vobject. of .thisinvention .to1:pr.Qvde .La protractor which enablesthejiser togauge; andV to pletangles directly in:themaenitiideszwhieh.apely to the variousprojeetions occurringinfaxonometric drawings .Where dimensions .f as Well as angles of the original object. represented arefdistorted or rhodied vdue `-to'gs ',dproj ection.

It is another object of thi finventiongtoqprovide an axonometric protractor which `'tiiroughits shape and the .arrangement ofthereierence or zero lines -of the :angular-graduation or graduations facilitates its vuse duegto fthe `,fact that` `a correetpesitionof. the protraetor with; respective theaxes` of the partculariaxonemetric; drawings-.s automatically obtained.

A further- .ebieet of the .intention censistszir. providingJ on one protractor'bcth airegllltriengil- 1&1' gadllfOn and DlleQItmQIe flllmftri :.01 mo dined Y graduations. .s that'gthe ;.modied.f.angle required to represent in the axonometric drawing a certain angle occurring on ,the representedobject may be read directly fremthe. protraetor,.and vice versa.

.Stillfa further .obieetnef this :invention'is fte provide ,anaxenemetrie inretraeteravvbienr iserevided With means permitting .togeause and. plotsecalled non-axonometrie -1inesineorreetleneth that maybe. fereshortened orlengthenedfwithrespect to the length'of theoriginal -gline onfthe represented .object ...depending :nnen .the angie which that particular line includes with` .One i of the4 axes of the.partieulartaxenemetrie.system.

Another object of theginvention consists infdevising an axonometric protraotor of the type described in the. preceding parasraphbut vprovided with means that Wonldpermit to yuse fthe-protractor independently of, the.v actualdrawing-.as a computing device similarly as a slide rule-'for converting actualv angles into the corresponding modified or projected anglesand.vicezversa, and

for convertingactual. dimensionsxinto .the correspending modifiedor projected. dimensions, .and viceversa.

More objects ofithe presentL invention-Will .become evident. from the followingi .descriptiom-.by way .of example, tof.. a numbenof: fpreferredembodiinents of i the invention.. reference` a'oeinglV had to the, accompanyingfdrawingsrin which Figs. 1, Zand 3..are`: diag-ramsintendedztoillustrate the specic features n of vaxonometric systems referred to .ein i= thisidescription;-and:more

particularly those ofsisometric," dimetricwandftri- A metric systems, .-respectively;

Figni'. is a. plan View of.A al fulhcircle protractor provided ,with anisometric graduation .anda rol-tatahle indexing membemin.. a polygonal :.frame,

.but in.r addition :provided .with.;an. index zcurreon 2 the-frame andwith a specialgraduationen Ythe indexingmemberpermittingtodeterminetheratio-Acf-,ioreshortening or lengthening of actual-,dimensions inconsequence ofthe isometricprojectien. ependine drenthe.aneuiardireetien of the particular dimension;

Fie.v 5 .isea'zverteal eress section, .net-.t0 ,sea-1e, taken alongfline-V-3V of Fig.4.

'Fier-'61s .ahlen View .0f another versenfeta protraeter as; vstiewriqbylie.. 4, the indexgcurvebeine constructed.: en thebasis of: logarithmic values reeresentinsthe abQve-mentioned raties,.;.and:the indexing member beinerrevided alsovvith. aelide rule arrangement; v

-1ig. -'7 is ya vertical Lcross section through the rotatable index memheralong line VII- Vllof Fig. 6.

"Fig 8 isafragmentary'planview end fFig. 9 isaeerrespendine cross-.sectional elevation showinga modification ofthe construction illustrated bv lilies.A 6 arida?- ylnihe; following descriptionv isometric, dirnetric and trimetric-systernsrand drawings are referred to. L'Inrorder to avoid,A misunderstandings and to shorten Ythe explanations, vthe .following statements and {defnitionsjare to beapplied `to .this specificationand t0 the claims.

,As NFig. 1 i implies, in Nan isometric drawing. or system thethree axes A,` B andiC are offsetagainst each-,othereqllally by each and therefore the scalesapplying ,to .each of :these axesareequal `toeaeh other andv so, are the angles ofA projection that apply ,to the planes `contained.between. .each pair'of axes.

In a dimetric system or drawing as symbolized bYEig, 2, only two of the angles between the. axes are equal. In .the .present .case the. actual. angles betweentheaxes .andthe corresponding angles, of projection havefheen chosen in. such a Way that -thescales along-the axes` A. .and C are equal and twice `aslargeas ;the scaleapphed to axis fB.

In a trimetric system, or drawing. the. angles hetweenthenthree axes. are. different from each othergand f so;` areV the .,angles.. .of projection and thevscalesgapplyng.tothe threeaxes. .The angles between the, axesfA, aBA and f C shown. inVv Fig.. 3` are calculatedon thepermissible .assumption that the scales -are: 1:1, on axis, A, .9:.1..on.axs1B., and .175:1Y en axisc.

'-lihe-.yI ious graduations shown .in the Idrawed jon the .above,..b.ut. may Yhe. varied tric-and trimetric .systems as .i they rare @given .onlyqloy'way., of. example.

11113 LS .if/.611 knownthat in .axonometric systems Whnzthe @rieles betweenthe. threeaxes are determined there is .Still room Afor different .arrangements of these.axes.,.with regard .tos-each other andrin relatonto the actual drawing. For .nstanee,.any. one :.of: thathreeeaxes may khear-- Yrangedfin 'vertical ,direction .on the drawingl and aeaacec the sequence or consecutive order of the axes A, B, C may be clockwise or anti-clockwise, whatever the particular case may call for. Only for simplifying the matter, in the following description and in the drawings uniformly that case has been elected in which the axis A is vertical and the consecutive order of A, B and C is anti.- clockwise.

Since any embodiment of this invention requires a solid body or frame adapted to be used on a drawing board like any other drawing instrument, repeatedly certainedges of such a frame are referred to. The term edges is not to be taken literally. If in the particular case that edge is used only for lining up or positioning the instrument on the drawing either by lining up the edge with a given line of the drawing or with an edge of another drawing instrument as for instance T-squares, straightedges, triangles or blades of drafting machines then other means that are not exactly an edge would be equivalent. For instance a line or a number of points in straight alignment marked on a frame inside its contour would serve the same purpose. Or for instance, the edge of the instrument might be notched out and may have only a number of projections that may be placed againstv a straightedge or the like so that the imaginary line connecting these projections would serve for positioning the instrument and rotatable member indicates a chosen angle A against the center-zero line of the particular instrument. Although the addition of a rotary member makes the instrument more expensive it certainly is of great advantage as angular lines can be drawn directly along the proper edge of that rotatable member while in any other case a point opposite one particular graduation mark would have to be marked on the paper and then connected separately with the particular central point.

Moreover, the protractors illustrated by Figs. 4 to 9 have the common feature of the frame being more or less polygonal or at least having edges that run at certain angles against the centerzero line of the particular graduations. This provision is of advantage because thereby the frame of the instrument can be very conveniently positioned so that the particular center-zero line is parallel with one of the axes of the pertaining plane of the particular axonometric projection.

The protractor according to Fig. 4 contains along the edge 69 of a circular opening 10 in a polygonal frame 1I, a regular 360 graduation 12 and a concentric isometric graduation 13. Both graduations are composed of two 180 graduations, one of them running clockwise and the other one anti-clockwise, the center-zero line being common to all of them. The lower part of the polygonal frame 1| has three edges 14, 'I5 and 16, each being at 120 relative to the adjoining edge. The center-zero line of the graduations is at relative to the base edge 15. Therefore, by placing any one of the edges 14, 'I5 or 'I6 against a T-square the center-zero line and the 90 mark of graduation 13 will always be positioned correctly so that the isometric graduation can be used properly in the corresponding planes AC, AB or BC, respectively, as indicated by the axis symbols arranged near every one, and relative to every one, of the said edges.

The rotary index member consists of a straight strip 'H extending over the graduations 'I2 and 'i3 and provided with two opposite guides 18 that have the shape each of a circular segment. As shown more clearly in Fig. 5 the segments or guides 'I3 engage by means of projecting tongues l a corresponding circular groove provided in edge Thereby a correct rotary movement of member 'il around the center 0l of the opening 'i0 and of the concentric graduations "I2, 13 is assured. The indexing edge 82 of member 11 extends through that central point 8l. The provision of the rotary member 'Il in this embodiment of the invention has the effect that edge 82 serves not only for drawing and gauging angular lines in any position of strip 'i1 relative to the center-Zero line, but the outer extension of edge 82 at the end of strip 'il overlapping the graduations 'l2 and I3 is useful for determining the relation between isometric angles and regular angles, and vice versa.

Fig. 4 shows that concentric to the center 8| an index curve 03 is provided on the frame 'Il between the central opening 'i0 and the graduation i3. This index curve 83 is designed in such a Way that the radial distance' of every point of its perimeter from the center Si is equal to a constant multiplied by the ratio of foreshortening or lengthening affecting, through the isometric projection, a given distance extending at the corresponding angle contained between the centerzero line and the radius through the particular point. In the present instance, the curve B3 is an isometric ellipse. In line with the basic principles of the isometric system, the radial distances to the points of the curve that are situated in direction to the zero, and 180 marks of the graduation, are equal to the chosen constant since in these selected directions there is neither foreshortening nor lengthening. The indexing edge 82 of the rotary member 11 is provided with one, or preferably two identical, graduations, E4 which, in the present case, is a linear scale representing the above mentioned ratio on the same basis which underlies the construction of curve 83. Therefore, in any position of member 17, the actual ratio applying to that particular angular direction indicated on scale 'I3 may be read directly on graduation 84 at the point of intersection between the curve d3 and the index edge 82.

It is evident that the just described feature is of great value. Up to now the so-called nonaxonometric lines, i. e. lines extending in directions not parallel with any one of the axonometric axes, could not be drawn to a denite scale nor scaled from a given axonometric drawing. Their length had to be determined indirectly by plotting or scaling their axonometric coordinates which is a very cumbersome and time-consuming operation. Now by means of the said index curve and the graduation on the index member the ratio in any angular direction within an axonometric plane can be quickly and correctly determined and the length at the scale of the drawing calculated by simple multiplication.

It is to be understood that the polar coordinates of the individual points of the index curve need not be determined by the product of a constant and the particular ratios, but instead of acoasee that constant a function may be used with the effect/that then of course the graduation 84 is not of linear nature. This may be useful in the case of applying the same principle to dimetric or trimetric systems in which cases the curve, if designed by using a constant as basis, would become very oblong, but could be shortened by using a certain function.

In any caseof a protractor that is provided with a rotary index member, it is advisable to arrange, along the index edge of such member, a linear graduation in units of length at the scale at which the particular drawingvis to be drawn. Such a graduation has to extend only over that portion of said index edge which spans the opening in the frame of the protractor. In order to simplify the drawings such graduations are not shown in the gures described so far, but is shown in Fig. 6 which is described further below.

While the examples described with referenceto Figs. 4, 6 and 8 are designed to deal with isometric problems only, it is obvious that they could as well be adapted analogously to dimetric and trimetric conditions. Such adaptations may either take care, by providing only one axonometric graduation and one index curve, of one of the various projections occurring in dimetric and trimetric systems, or they might comprise a number of different axonoinetric graduations and a corresponding number of index curves.

Fig. 6 illustrates a modied version of the pro- A a constant may become very inconveniently obs long. Instead of substituting a certain function for the constant, the indexcurve may be constructed in such a way that the radial distance of any one of its points is equal to the product of a constant and the logarithm of `the ratio of foreshortening or lengthening occurring in the angular direction of that particular point.

In Fig. 6 a protractor is shown which is generally similar to the one illustrated by Fig. 4i. Thereforethe same numerals are applied to like parts. Besides an isometric graduation 13 the frame 'il is provided with a regular graduation l2, both concentric to the circular opening lo. A logarithmic index curve |04 is arranged concentric with and between graduations 12 and 13. The rotary index member |05 has an indexing edge l extending through the center |07 o-f roitation. This edge |55 is provided, in this example, with a regular inch graduation |00. In addition the index member |05 is provided with means resembling a slide rule. A movable strip |09 is slidably guided between two narrow strips H and that are attached to the member E parallel with edge |06. The cross-section Fig. 5 shows the details of this arrangement. The movable strip |09 has 'an extension H2 towards one side which is provided with an indexing edge |3.of sufficient length to overlap the graduation 7-3 no matter how farthe strip-lha is moved one way or the other within the' range of this instrument. Besides the edge H3 always forms an extension of, or is inV alignmenty with, the edge |06. On account of this, the member |05-may be set with its edge |05 in any angularposition with respect to graduation '|32 or 1.2'. With referenoe to graduation 'l2 zero marks or indexlines Hltare provided in line with edgeAv |00.; on the member |05. If desired a Vernier H5V ymay be' added to one of the marks lli.

The strip H0 is provided along its inner edge 6 with a logarithmic graduation H6 based on the same constant or scale on which the curve |04 is constructed. This means that if, for instance, a unit of length A has been chosen to represent the logarithm of an actual dimension R=10 on member |09 (scale HDthen the index curve |04 must be constructed so that, along its perimeter the radial center distance of every one of its points representsthe logarithm of those coefficients which indicate the percentage of foreshortening or lengthening of the actual dimensions of lines at the particular angular position, said logarithme being plotted at the same scale which results in representing theY logarithm of R=10 by the chosen unit of' length A. It is advisable to extend the scale H6 downward be.- yond the value 1 and upward beyond the value l0 which latter, in fact, is used in the well known way also as 1. The strip |05 is provided along its edge facing the strip H0, with a logarithmic graduation constructed on exactly thesame scale as H6 so that these two graduations or scales may be used like an ordinary slide rule. The edge H3 of the slide ex tension H2 provided with an index mark H3 in such a position that when the rotary member |05 is set to the angular position zero or90f on scale '53, and when thetwo logarithmic graduations H and Hl are brought into complete alignment, the index H8 lines up exactly with the curve |04 at its point of intersection with edge H3.

In practice, the rotary member |05Ymay be set to any desired angular position and, in such position, the index H0 may be brought into register with the corresponding point of the curve |04.- Then, except for the above-mentioned selected positions, the marks l of graduation H1 will indicate on the opposite scale i5 the ratio of foreshorteningror lengthening, as the case may be, that applies to lines in the particular angular direction. However, this ratio needv not be read. In the example illustrated the angular position is 45 on the isometric scale 13, therefore the ratio.

is 1.225. Suppose, however, a dimension of 3" is Ito be plotted along edge |00 in that direction, the user will read opposite the mark 3 of graduation the value 3.675 on graduation HE. This would then be, in inches, the length of a line to be drawn along edge litt by means of graduation |08 in order to represent correctly the dimension 3" at the given angle. The analogous procedure applies in reverse if the length.

of a non-isometric line in an isometricr drawing is to be gauged or scaled. rf'he slide member |09 is held and guided by bevel and/or groove engagement with strip Iii' and another backing strip i attached thereto.

As shown by Figs. 8 and 9 in this embodimentof the invention the logarithmic curve |04 may be replaced by a groove H9 in which a guide pin |20 provided on the slide extension H2. instead of the index H8 would be automatically guided so as to control the lengthwise mover'nentl or" slide |00 during a rotary movement of the member |05. Obviously, thisV version of the linstrur'nent facilitates and speeds up the operation and pre-` vents errors.

While I have described la number of' selected and preferred embodiments of my invention, I wish it to be understood that I do not wish to bev limited to the details thereof. asmany. variations.

and modifications, substitutions of equivalents and combinations of the described features may be found and used by those skilled in the art without departing from the gist and scope of the present invention.

What I claim is:

1. A protractor comprising a frame, means on the frame indicating a central point, an angular scale arranged thereon related to said central point adapted to indicate angles in such modified magnitudes as are determined by their projection in an axonometric system, said frame being provided, in addition to said angular scale, with at least one index curve on said frame related to said angular scale, said index curve being determined at every point of its perimeter by its being situated on a radial line from said central point to a point of said angular scale and at a radial distance from said central point equal to a constant multiplied by the ratio of foreshortening or lengthening affecting through the particular projection a given distance extending at the corresponding angle, with the protractor in a position predetermined for one plane of the projected object, said frame being provided with an indexing member adapted to be rotated with respect to said frame and in a plane parallel with that of the frame, the center of rotation coinciding with said central point of said angular scale, said member being provided with an index having at least one extended portion related to the center of rotation and to said scale so as to be adapted to measure and indicate angles one leg of which is a line from said central point to a point of said scale; said rotatable member being also provided, along its index, with a graduation adapted to intersect, during the rotation of said member, with said index curve and to indicate, in any angular position the ratio of foreshortening or lengthening applying to that angular position.

2. A protractor comprising a frame, means on the frame indicating a central point, an angular scale arranged thereon related to said central point adapted to indicate angles in such modified magnitudes as are determined by their projection in, an axonometric system, said frame being provided, in addition to said angular scale, with at least one index curve on said frame related to said angular scale, said index curve being determined, at every point of its perimeter, by its being situated on a radial line from said central point to a point of said angular scale and at a radial distance from said central point equal to a constant multiplied by the logarithm of the ratio of foreshortening or lengthening affecting through the particular projection a given distance exending at the corresponding angle, with the protractor in a position predetermined for one plane of the projected object, said frame being provided with an indexing member adapted to be rotated with respect to said frame and in a plane parallel with that of said frame, the center of rotation coinciding with said central point of said scale, said member being provided with an index portion related to the center of rotation and to said scale so as to be adapted to measure and to indicate angles one leg of which is a line from said central point to a point of said scale, and the said index portion of said rotatable ymember being provided with a graduation in units of length; said rotatable member being also provided with a fixed logarithmic graduation and with a sliding member provided with a logarithmic graduation to the same scale, both logarithmic graduations being `parallel with the said unit of length graduation, said sliding member being provided with an index mark adapted to be brought into coincidence with the intersection of Vsaid curve with the line connecting the said central point with the corresponding point of the said related modied angular graduation, so that in any angular position of the said rotatable member the index of the slide member may be aligned with the pertaining point of said index curve in order to set thereby the slide member and thus its logarithmic graduation, with respect to the fixed logarithmic graduation, to the ratio between original lengths and their counterparts in the pertaining projection, whereby the projected length may be read from the xed logarithmic graduation.

3. A protractor as speciiied in claim 2, in which the index line in the form of a logarithmic curve is an edge of any kind including that of a groove provided on said frame, and the index mark on the slide member comprises means adapted-to be guided along said edge on a path equivalentv to and conforming with said logarithmic curve while said rotatable `member is brought into various angular positions with respect to said frame.

PAUL F. BOEHM.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date D. 141,882 Matson July 31, 1945 570,977 Belcher Nov. 10, 1896 796,417 Enberg Aug. 8, 1905 1,422,925 Carter July 18, 1922 1,461,335 Vosler July 10, 1923 1,561,462 Cram Nov. 17, 1925 1,682,035 Clark Aug. 28, 1928 1,723,517 McFadden Aug. 6, 1929 2,039,333 Musham May 5, 1936 2,331,298 Bennett Oct. 12, 1943 2,398,143 Jaediker Apr. 9, 1946 2,422,745 Ost June 24, 1947 FOREIGN PATENTS Number Country Date 563,313 Great Britain Aug. 9, 1944 526,005 Great Britain Sept. 9, 1940 598,911 Germany June 21, 1934 379,984 Germany Sept. 1, 1923 352,988 Italy Oct. 1, 1937 389,995 France July 17, 1908 488,874 France Aug. 1, 1918 OTHER REFERENCES Pages 80, 8l, 132, 134 of Aero Digest, July 1, 1944, containing an article entitled Photography Simpliies Trirnetric Drawing Technique, by W. G. Wilkinson and H. C. Bartholomew.

Pages 147 to 152 and 196 of Machine Design, vol. 17, February 1945, containing an article entitled Trimetric Drawing- Its Theory and Technique, by G. F. Bush.

Treatise on Iscmetrical Drawing by T. Sopwith, pp. -98 and 136 to 138 and plates XI and XVI. A. D. 1838.

A Treatise on Projection, by P. Nicholson, London 1837, pp. -123, plates 48 and 49.

Page 277 of catalogue of Eugene Dietzgen Co., 218 E. 23rd St., New York, N. Y. 

